By applying my own extension of Pierce’s semiotics to the question, (ie. the quaternary logic of the three active epistemes) it is seen that the truths of geometry are a priori and self-evident, while the ‘truths’ of arithmetic require us to adopt synthetic argumentation (via the assumption of the coherency of infinite addition and infinite series, the assumption that it makes sense to infinitely repeat the operation of adding 1 to a starting number to create the number line, which is not a self-evident truth) that falls back to axiomatics under examination, (namely, the axiom of choice) leading eventually to an ‘entangled semantics’ between the two different levels of abstract structure that has further entangled the fundamental mathematical operations and concepts with one another and so prevented the semiotic chain from fully completing the loop through the three epistemes needed to clarify and extend meaningful representations of objects, a failure resulting in the production of imponderable questions that don’t actually mean anything, since such questions, like that involved in the RZF, arise only from a confused semantics. I was naturally led to group theory in the search for some means of disentangling the confused semantics of the mathematical relations encoded by addition, multiplication, etc., given the fact that the sums of an infinite number of groups require that the constituents always have finite non-zero elements, whereas direct products of sets are not similarly bounded, and I then discovered that Mochizuki has sought in precisely this domain, attempting to disentangle these relations through some extensions of Teichmuller-space and Galois groups.

This is all an ancillary digression from the main theory of the epistemes, making up a few pages in the footnotes to a 60 page essay I’m not going to post in this thread because it’s just going to be overwhelming, but it is nonetheless useful by itself, even to those with no interest in math, as a demonstration of how the same semiotic process can be shown to be occurring in disciplines as apparently unrelated as philosophy, semiotics, psychoanalysis, and pure math. I will begin with a couple pages from that larger essay though, a few pages that summarize what an episteme is and how the ‘semiogenetic loop’ works by cycling through them to produce new meaning.

Elsewhere,

The ‘entangled semantics’ characterizing modern maths (which all boils down to set-theory, a bunch of postmodern garbage riddled with unresolved paradoxes that mathematicians, because they couldn’t solve them, just threw their hands up at, falling back to defending themselves through arbitrary axioms) has led to a blockage of the semiogenetic loop, and the same problem is at work in essentially every single human discipline: philosophy, ethics, semiotics, math, even the natural sciences, etc. Through the metaphilosophy of the epistemes, I have sought to bring the underlying process being blocked, and through which all meaning is produced, into the light as itself a new object of thought; it is simultaneously what philosophy is, how philosophy philosophizes, and that about which philosophy philosophizes. Through it, this metaphilosophy, all human knowledge can be reconciled to and integrated with all other human knowledge, just as I have done here with Schelling’s transcendental idealism, Arabic zairja mysticism, Peircean semiotics, Lacanian psychoanalysis, pure maths and group theory, M. Ponty’s phenomenology, Bataille, etc. (The epistemes doubly serve as a methodology for learning; it is by actually using the process of the semiogenetic loop that I was able to convert one field of discourse into another, teaching myself something like pure math by translating it into a discourse I already knew like psychoanalysis or transcendental idealism. This method and technique dramatically accelerates learning itself, allowing one to rapidly gain access to any field of study they want.) And, in this grand integration of all human knowledge, so all the “problems” in the disparate fields of discourse are revealed to be expressions of the one fundamental problem the epistemes address.